The rocket equation and delta-v

Mu1903, Konstantin Tsiolkovsky, mudzidzisi wechikoro akataura zvisina kujeka, akanyora pasi equation iyo inoramba ichienzanisa marudzi ese erocket. Izvi zvinotsanangura kuti nei Falcon 9 ichishandiswa ne89% yepropellant, nei payload iri chete muzana rakawanda rehuwandu hwepakutanga, uye nei marockets achisiya zvinhu zvavo panzira.

Yese rocket ndeimwe racing pakati pesimba iwe uchida uye masendimita iwe unofanira kutakura kuti uwane.

Ona

A rocket inofamba nekuvatuka maseva kumashure. Throw zviri nyore, kana throw zvakawanda, uye iwe kuenda nekukurumidza. Kune matambudziko: mafuta asingazivikanwe kuti achiri kusvibiswa, anofanirawo kuendeswa uye kukwira. Izvi zvinoita kuti kuwanikwa kuri logarithmic: kuti udzore simba rakafanana, unofanirwa kusvibisa mafuta, kwete kuisa.

Delta-v (Δv, “change in velocity”) ndiyo mari yendege dzepasi. Ichi chirongwa chinopa mutengo mukm/s:

• Kutanga kubva panyika kusvika kumahombekombe: 9.4 km/s, kusanganisira kushaya simba.
• Low orbit to geostationary orbit: about 3.9 km/s.
• Low orbit kudzokera kuMars: 3.6 km/s.

Roketi yemari ndeyekuti ndezvipi Δv ayo masimba, mafuta uye maseru anogona kupa.

_Zvinyorwa

Δv = I_sp · g₀ · ln(m₀ / m_f)

• I_sp: specific impulse, chiyero chekushanda kwechigadzirwa mumasekondi (kubuda kwemhepo kuparadzwa ne g₀).
• g₀ = 9.80665 m/s², standard gravity.
• m₀: masendimita pakutanga kwekupisa; m_f: masendimita pakupera.

Mufananidzo wekutanga neyakagadzirwa rocket (Isp 348 s): yakazara, inorema makirogiramu 112, kusanganisira 15-makirogiramu payload; pasina propulsant, pamusoro 19 makirogiramu. Δv = 348 × 9.81 × ln(112 / 19) ≈ 6.0 km/s. Chikamu chekutanga chinowedzera zvimwe zvinhu.

A chete chiitiko nechiuru ratio ye10 uye Isp 350 s anopa chete 7.9 km / s, kwete zvakakwana kuti orbit kana kushaya zvinonzi, uye chivakwa kuti ndiro chete 10% yemutengo yakanga iri nyore zvikuru. Izvi ndizvo zvinoita kuti rocket iite makiromita makumi maviri nemana kana kupfuura.

Munyori

Staging inowedzera huwandu hwemafuta. Yechikwata chemotokari,

Δv_total = I₁ g₀ ln(m₁/m_f₁) + I₂ g₀ ln(m₁₂/m_f₂)

apo yekupedzisira-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-yekutanga-ye Kuvandudza kuparadzana pakati pezvirongwa (neimwe Isp, zvakaenzana Δv pachikamu) ndechimwe chematambudziko ekare: payload fraction inokwira nesimba neDv yaunoda, izvo zvinoita kuti kuderedza Δv kuenda kumaorbit nemazana mashoma emamita / s (kutanga kumabvazuva, pedyo neEquator) zviite sezvakakosha.

Equationwo ano explicates pfungwa ye reusable yekutanga zvirongwa: ivo kukwirazve kushandisa mafuta kuti kunge zvakanga payload simba, trading a few percent of payload kuti kwete kubvisa yakanyanya mutengo chikamu cherocket.